To pick some mangoes from a tree inside seven walls with seven guards,
you tell each guard that you'll give him half of the mangos you have, but
he must give you back one mango. What's the minimum number of mangos you
must pick to have at least one mango left?

A magic dragon has 3 heads and 3 tails. A knight with a magic sword
can make four types of cuts--one head, two heads, one tail, or two
tails. For each type of cut, the dragon regrows one head, nothing,
two tails, or one head respectively. The knight must remove all
heads and tails to slay the dragon. What's the fewest number of cuts
he can make?

Seven monkeys spend the day gathering coconuts. As night falls, they
gather all the coconuts into one pile and agree to divide them up evenly
in the morning. At 12:00pm one monkey gets up and divides the pile of
coconuts into seven piles with one left over...